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Ms. Barton has four children. You are told correctly that [#permalink]

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02 Jun 2003, 11:55

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Ms. Barton has four children. You are told correctly that she has at least two girls but you are not told which two of her four children are those girls. What is the probability that she also has two boys?

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03 Jun 2003, 02:54

The answer is A.
Since we know for sure that there are at least two girls out of four children, the question can be rephrased as "what is the probability of having two sons out of two children?" Assuming that both son and daughter are equally likely, we have the answer as 1/4
QED
_________________

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28 Jan 2004, 08:36

Probability = desired_events/Total_events

total_events = 2G + 3G + 4G = 2B + 1B + 0B

This is a tricky question boss. The initial statement Ms Barton has two girls misleads you. If she has 4 children and two are girls then definitely other two are boys ( assuming no in between ). This is indirect way of asking what is the probability that out of 4 children 2 are boys.

I hope it is clear.

Last edited by anandnk on 30 Jan 2004, 07:43, edited 2 times in total.

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29 Jan 2004, 15:26

:oops:

the answer is D because its soooo very simple....the probability that out of the other two children (we already know that two are girls) both are boys is 1/2 as in case of any one of the two being a girl the probability does not hold

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01 Feb 2004, 00:52

Firstly I thought that it is A. But after anandk's explanations I have some doubt. But still don't understand his explanation fully.
We were told that 2 out of 4 children are girls. Which left us with the question " What is the probability of 2 of the rest children are boys.
Probability that 3d child is boy 1/2 so probability of 4th child is boy also 1/2. By using formula we got 1/2*1/2=1/4.

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03 Feb 2004, 06:11

ABNY2002 wrote:

Ms. Barton has four children. You are told correctly that she has at least two girls but you are not told which two of her four children are those girls. What is the probability that she also has two boys?

(A) 1/4(B) 3/8(C) 5/11(D) 1/2(E) 6/11

This is a question that I submitted a long time ago.

Anand is correct.

This is a question in "conditional probability".

Two ways to solve it:

1) first reduce the "possible" set to match the condition. We know that barton must have at least two girls. Of the 16 possible arrangements of children from youngest to oldest, only 11 qualify. Hence there are 11 possible arrangement of kids. Of those 11 exactly 6 have 2 boys. Hence, the probability is 6/11.

2) The "formula" for conditional probability is "prob without the condition" divided by "the probabllity of the condition". Hence, the odds of getting exactly 2 boys and 2 girls out of the sixteen possible is: 6/16. (BBGG, BGBG, BGGB, GGBB, GBGB, GBBG.), The probability of the condition (at least 2 girls) is 11/16 (16 less 5: BBBB, BBBG, BGBB, BBGB, GBBB).